Inhomogeneous distribution of droplets in cloud turbulence
Abstract
We solve the problem of spatial distribution of inertial particles that sediment in turbulent flow with small ratio of acceleration of fluid particles to acceleration of gravity . The particles are driven by linear drag and have arbitrary inertia. The pair-correlation function of concentration obeys a power-law in distance with negative exponent. Divergence at zero signifies singular distribution of particles in space. Independently of particle size the exponent is ratio of integral of energy spectrum of turbulence times the wavenumber to times numerical factor. We find Lyapunov exponents and confirm predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include typical case of water droplets in clouds. This significant progress in the study of turbulent transport is possible because strong gravity makes the particle's velocity at a given point unique.
Keywords
Cite
@article{arxiv.1409.6819,
title = {Inhomogeneous distribution of droplets in cloud turbulence},
author = {Itzhak Fouxon and Yongnam Park and Roei Harduf and Changhoon Lee},
journal= {arXiv preprint arXiv:1409.6819},
year = {2015}
}
Comments
6 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1409.5856, text revisions